SRC/ssbev_2stage.f(3)

📦

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🦋 SRC/ssbev_2stage.f(3) 🦋

okay bestie so this is a page from the Library Functions Manual (which is to say: the LAPACK gang's docs), and it's all about one lil subroutine that wants to find your eigenvalues for you. band matrix edition. ✨

✨ NAME ✨

SRC/ssbev_2stage.f — this is literally the file, that's the name, no notes 💅

🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine ssbev_2stage (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work,
    lwork, info)

SSBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices 🫶

🎀 Function/Subroutine Documentation 🎀

`subroutine ssbev_2stage`

subroutine ssbev_2stage (character jobz, character uplo, integer n, integer
    kd, real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) w,
    real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work,
    integer lwork, integer info)

SSBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices 👑

💖 Purpose: 💖

!>
!> SSBEV_2STAGE computes all the eigenvalues and, optionally, eigenvectors of
!> a real symmetric band matrix A using the 2stage technique for
!> the reduction to tridiagonal.
!>

🌈 Parameters 🌈

JOBZ

!>          JOBZ is CHARACTER*1
!>          = 'N':  Compute eigenvalues only;
!>          = 'V':  Compute eigenvalues and eigenvectors.
!>                  Not available in this release.
!>

heads up bestie: 'V' is not available in this release 😭 so it's giving "eigenvalues only" era for now

UPLO

!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>

N

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

KD

!>          KD is INTEGER
!>          The number of superdiagonals of the matrix A if UPLO = 'U',
!>          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
!>

AB

!>          AB is REAL array, dimension (LDAB, N)
!>          On entry, the upper or lower triangle of the symmetric band
!>          matrix A, stored in the first KD+1 rows of the array.  The
!>          j-th column of A is stored in the j-th column of the array AB
!>          as follows:
!>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
!>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
!>
!>          On exit, AB is overwritten by values generated during the
!>          reduction to tridiagonal form.  If UPLO = 'U', the first
!>          superdiagonal and the diagonal of the tridiagonal matrix T
!>          are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
!>          the diagonal and first subdiagonal of T are returned in the
!>          first two rows of AB.
!>

she gets overwritten on exit, ok?? don't come for her 💀

LDAB

!>          LDAB is INTEGER
!>          The leading dimension of the array AB.  LDAB >= KD + 1.
!>

W

!>          W is REAL array, dimension (N)
!>          If INFO = 0, the eigenvalues in ascending order.
!>

Z

!>          Z is REAL array, dimension (LDZ, N)
!>          If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
!>          eigenvectors of the matrix A, with the i-th column of Z
!>          holding the eigenvector associated with W(i).
!>          If JOBZ = 'N', then Z is not referenced.
!>

if JOBZ = 'N' then Z is literally not referenced. she's not invited to the function 💅

LDZ

!>          LDZ is INTEGER
!>          The leading dimension of the array Z.  LDZ >= 1, and if
!>          JOBZ = 'V', LDZ >= max(1,N).
!>

WORK

!>          WORK is REAL array, dimension LWORK
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
!>

LWORK

!>          LWORK is INTEGER
!>          The length of the array WORK. LWORK >= 1, when N <= 1;
!>          otherwise
!>          If JOBZ = 'N' and N > 1, LWORK must be queried.
!>                                   LWORK = MAX(1, dimension) where
!>                                   dimension = (2KD+1)*N + KD*NTHREADS + N
!>                                   where KD is the size of the band.
!>                                   NTHREADS is the number of threads used when
!>                                   openMP compilation is enabled, otherwise =1.
!>          If JOBZ = 'V' and N > 1, LWORK must be queried. Not yet available.
!>
!>          If LWORK = -1, then a workspace query is assumed; the routine
!>          only calculates the optimal size of the WORK array, returns
!>          this value as the first entry of the WORK array, and no error
!>          message related to LWORK is issued by XERBLA.
!>

quick math moment bestie: dimension = (2KD+1)*N + KD*NTHREADS + N — and NTHREADS is the number of threads used when openMP compilation is enabled, otherwise =1 ✨

also LWORK = -1 means workspace query — she only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA 🫶

lowkey important: if JOBZ = 'V' and N > 1, LWORK must be queried — not yet available 🙈

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>          > 0:  if INFO = i, the algorithm failed to converge; i
!>                off-diagonal elements of an intermediate tridiagonal
!>                form did not converge to zero.
!>

INFO = i > 0 means the algorithm failed to converge and i off-diagonal elements of an intermediate tridiagonal form did not converge to zero. it's giving tragedy 😭

👑 Author 👑

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

🧚 Further Details: 🧚

!>
!>  All details about the 2stage techniques are available in:
!>
!>  Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
!>  Parallel reduction to condensed forms for symmetric eigenvalue problems
!>  using aggregated fine-grained and memory-aware kernels. In Proceedings
!>  of 2011 International Conference for High Performance Computing,
!>  Networking, Storage and Analysis (SC '11), New York, NY, USA,
!>  Article 8 , 11 pages.
!>  http://doi.acm.org/10.1145/2063384.2063394
!>
!>  A. Haidar, J. Kurzak, P. Luszczek, 2013.
!>  An improved parallel singular value algorithm and its implementation
!>  for multicore hardware, In Proceedings of 2013 International Conference
!>  for High Performance Computing, Networking, Storage and Analysis (SC '13).
!>  Denver, Colorado, USA, 2013.
!>  Article 90, 12 pages.
!>  http://doi.acm.org/10.1145/2503210.2503292
!>
!>  A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
!>  A novel hybrid CPU-GPU generalized eigensolver for electronic structure
!>  calculations based on fine-grained memory aware tasks.
!>  International Journal of High Performance Computing Applications.
!>  Volume 28 Issue 2, Pages 196-209, May 2014.
!>  http://hpc.sagepub.com/content/28/2/196
!>
!>

three whole papers, bestie. the reading list is stacked 📚✨

Definition at line 202 of file ssbev_2stage.f.

⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code. (she's a bot, but make it fashion 🤖💅)

and that's the whole page!! mwah 💖

signing off from LAPACK, Version 3.12.0, dated SRC/ssbev_2stage.f(3) — slay, stay convergent, and query your LWORK bestie 🎀🦋

📦 where this page comes from

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